Sr Examen
Integral de (sqrt(2)*sin(t)^3)*(-6*sqrt(2)*sin(t)*cos(t)^2) dt
Solución
Ha introducido
[src]
pi -- 3 / | | ___ 3 ___ 2 | \/ 2 *sin (t)*-6*\/ 2 *sin(t)*cos (t) dt | / pi -- 4
$$\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{3}} \sqrt{2} \sin^{3}{\left(t \right)} - 6 \sqrt{2} \sin{\left(t \right)} \cos^{2}{\left(t \right)}\, dt$$
Integral((sqrt(2)*sin(t)^3)*(((-6*sqrt(2))*sin(t))*cos(t)^2), (t, pi/4, pi/3))
Respuesta (Indefinida)
[src]
/ | 6 6 5 5 2 4 4 2 | ___ 3 ___ 2 3 3 3*t*cos (t) 3*t*sin (t) 3*sin (t)*cos(t) 3*cos (t)*sin(t) 9*t*cos (t)*sin (t) 9*t*cos (t)*sin (t) | \/ 2 *sin (t)*-6*\/ 2 *sin(t)*cos (t) dt = C + 2*cos (t)*sin (t) - ----------- - ----------- - ---------------- + ---------------- - ------------------- - ------------------- | 4 4 4 4 4 4 /
$$\int \sqrt{2} \sin^{3}{\left(t \right)} - 6 \sqrt{2} \sin{\left(t \right)} \cos^{2}{\left(t \right)}\, dt = C - \frac{3 t \sin^{6}{\left(t \right)}}{4} - \frac{9 t \sin^{4}{\left(t \right)} \cos^{2}{\left(t \right)}}{4} - \frac{9 t \sin^{2}{\left(t \right)} \cos^{4}{\left(t \right)}}{4} - \frac{3 t \cos^{6}{\left(t \right)}}{4} - \frac{3 \sin^{5}{\left(t \right)} \cos{\left(t \right)}}{4} + 2 \sin^{3}{\left(t \right)} \cos^{3}{\left(t \right)} + \frac{3 \sin{\left(t \right)} \cos^{5}{\left(t \right)}}{4}$$
Gráfica
Respuesta
[src]
1 pi - - - -- 4 16
$$- \frac{1}{4} - \frac{\pi}{16}$$
=
=
1 pi - - - -- 4 16
$$- \frac{1}{4} - \frac{\pi}{16}$$
-1/4 - pi/16
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.